Boundary-Maintaining Self-Organizing Systems under Finite Capacity: Maintenance Load, Phase-C Collapse, and Invariant Selection

摘要

Paper also available at https://philarchive.org/rec/WUBSSU Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-N1 develops a complex-systems bridge for Active Finite Distinction Systems. It translates the FDS formal core into a normal-form account of boundary-maintaining self-organization under finite representational capacity and finite resource budgets. In this paper, a self-organizing system is not merely a system that becomes structured. It is a finite system whose internal updates are causally relevant to future boundary-maintenance loss. The paper therefore distinguishes active self-organization from passive stability, spontaneous pattern formation, or unconstrained order production. The model distinguishes structural complexity K(t) from maintenance load LM(t), operationalizes effective organizational capacity Corg(t), introduces resource-gated pruning, treats externalization as an accounting-boundary shift that can clog the environment, and defines a Phase-C catastrophic-feedback regime in which boundary loss reduces resource intake and accelerates collapse. The main theorem states that an active-boundary finite system with positive deficit-driven load pressure, finite resource input, and eventually resource-exceeding maintained load cannot remain indefinitely in unbounded Phase-A growth without pruning, compression, externalization, task relaxation, invariant stabilization, resource expansion, automation, or collapse. Invariant-supported persistence is connected to a Phase-B survival score based on boundary utility, predictive utility, maintenance cost, verification cost, and refresh cost. The paper also provides a domain bridge template for applying the model to protocells, neural systems, robots, organizations, civilizations, or other candidate active-boundary systems. The accompanying replication package includes deterministic synthetic simulations, figures, CSV outputs, LaTeX source, and Python code. The simulations illustrate Phase-A/Phase-B/Phase-C trajectories, operational organizational capacity, pruning viability windows, externalization clogging, bounded self-organization regimes, invariant-residue selection, active-boundary ablation, and domain bridge templates. Scope. This paper does not claim that all self-organizing systems are alive, intelligent, conscious, optimal, or oscillatory. It does not claim that every boundary is active or that every pattern is self-organizing. Its contribution is a finite-capacity normal form and mapping protocol for boundary-maintaining self-organization.